We employ a recently proposed model [Murisic et al., “Dynamics of particle settling and resuspension in viscous liquids,” J. Fluid. Mech. 717, 203–231 (2013)] to study a finite-volume, particle-laden thin film flowing under gravity on an incline. For negatively buoyant particles with concentration above a critical value and buoyant particles, the particles accumulate at the front of the flow forming a particle-rich ridge, whose similarity solution is of the rarefaction-singular shock type. We investigate the structure in detail and find that the particle/fluid front advances linearly to the leading order with time to the one-third power as predicted by the Huppert solution [H. E. Huppert, “Flow and instability of a viscous current down a slope,” Nature 300, 427–419 (1982)] for clear fluid (i.e., in the absence of particles). We also explore a deviation from this law when the particle concentration is high. Several experiments are carried out with both buoyant and negatively buoyant particles whose results qualitatively agree with the theoretics.
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March 2015
Research Article|
March 09 2015
Rarefaction-singular shock dynamics for conserved volume gravity driven particle-laden thin film
L. Wang;
L. Wang
a)
Department of Mathematics,
University of California Los Angeles
, 520 Portola Plaza, Los Angeles, California 90095, USA
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A. Mavromoustaki;
A. Mavromoustaki
Department of Mathematics,
University of California Los Angeles
, 520 Portola Plaza, Los Angeles, California 90095, USA
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A. L. Bertozzi;
A. L. Bertozzi
Department of Mathematics,
University of California Los Angeles
, 520 Portola Plaza, Los Angeles, California 90095, USA
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G. Urdaneta
;
G. Urdaneta
Department of Mathematics,
University of California Los Angeles
, 520 Portola Plaza, Los Angeles, California 90095, USA
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K. Huang
K. Huang
Department of Mathematics,
University of California Los Angeles
, 520 Portola Plaza, Los Angeles, California 90095, USA
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a)
Author to whom correspondence should be addressed. Electronic mail: [email protected]
Physics of Fluids 27, 033301 (2015)
Article history
Received:
February 15 2014
Accepted:
January 13 2015
Citation
L. Wang, A. Mavromoustaki, A. L. Bertozzi, G. Urdaneta, K. Huang; Rarefaction-singular shock dynamics for conserved volume gravity driven particle-laden thin film. Physics of Fluids 1 March 2015; 27 (3): 033301. https://doi.org/10.1063/1.4913851
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